Now that we have defined uncertainty and given it a unit of measure, we shall put
information in terms of uncertainty.
Let us examine our boxes with the blue ball again, but for simplicity, let's say
there are just eight boxes. At the start, before the ball's location is known,
there is an uncertainty of 3 bits (
)
[equations (2)
and
(13)].
After the ball has been
located, there is no uncertainty as to where the ball is. After all, you are
staring right at it. Since your uncertainty has gone from 3 bits to 0 bits,
you have GAINED 3 bits of information.

Now suppose we play the guessing game, but that
I refuse to tell you the answer to the last yes-no
question you ask. Before playing the game your uncertainty is 3 bits, but
after the game is over, you still don't know which box the blue ball is in.
Because you are still uncertain by 1 bit, you learned from me
only 3 - 1 = 2 bits.
In other words,
the uncertainty (H) before the input is received
minus the uncertainty after
it is received is
the information you gained (R):

Words from the Unix
dictionary, /usr/dict/words, were aligned by their first letter.
Vowels are darker and consonants are lighter.
In color versions of this paper, vowels are red, consonants are green
and the letter Y is in blue.

Figure 4:
Sequence logo of words in this paper.

Words were aligned by their first letter.
In color versions of this paper, vowels are red, consonants are green
and the letter Y is in blue.